Multi-Recursive Constraint Demotion

A signi cant source of di culty in language learning is the presumed \incompleteness" of the overt information available to a language learner, termed here an `overt form', when they hear an utterance. The complete structural description assigned to an utterance by linguistic analysis includes representational elements not directly apparent in the overt form, but which play a critical role in linguistic theory. Because the central principles of linguistic theory, including those determining the space of possible human grammars, make reference to these elements of `hidden structure', recovering them is necessary if the overt data are to be brought to bear on the task of determining the correct grammar. Hidden structure, although not directly perceivable, need not be a great di culty if it can easily be reconstructed based upon the overt form. Hidden structure becomes a problem when the overt form is ambiguous. If a given overt form is consistent with two or more di erent full structural descriptions, then the correct structural description cannot be determined from the information in that overt form alone. Presumably, other data, from other overt forms, is necessary to determine the correct structural description. In Optimality Theory (Prince and Smolensky, 1993), learning a grammar means nding a correct ranking for the universal constraints. The learner, given a collection overt forms (presumed to be the overt re exes of grammatical utterances), must arrive at a ranking of the constraints such that, for each overt form, there is a matching structural description which is optimal for some input under that ranking. Tesar and Smolensky (Tesar and Smolensky, to appear) have demonstrated that, given the correct full structural descriptions, a constraint ranking can be determined e ciently which makes all of those structural descriptions optimal. Thus, if the problem of hidden structure can be overcome, constraint rankings can be learned. Recent work by Tesar on language learning in Optimality Theory has used an iterative strategy to approach the problem of determining hidden structure (Tesar, to appear) (Tesar, 1997). The strategy processes overt forms in serial fashion, one at a time. One notable property of that work is that, when the processing of an overt form is complete, the procedure retains as information only a single hypothesized constraint hierarchy. Upon receipt of an overt form, the algorithm modi es its hypothesized constraint ranking as necessary to accommodate the overt form, but then retains only the resulting constraint hierarchy as information when moving on to the next overt form. This behavior is standard practice in what is known as the \language learnability in the limit" framework(Gold, 1967). One motivation for this type of limitation is to avoid learning procedures which remember an unbounded number of utterances. However, limiting the